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A modified Broyden family algorithm with global convergence under a weak Wolfe-Powell line search for unconstrained nonconvex problems

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Abstract

The Quasi-Newton method is one of the most effective methods using the first derivative for solving all unconstrained optimization problems. The Broyden family method plays an important role among the quasi-Newton algorithms. However, the study of the convergence of the classical Broyden family method is still not enough. While in the special case, BFGS method, there have been abundant achievements. Yuan et al. (Appl Math Model. 47:811–825, (2017)) presented a modified weak Wolfe-Powell line search and obtained the convergence of BFGS method for general functions under this line search. Motivated by their works, a new modified weak Wolfe-Powell line search technique is proposed for unconstrained problems. We assume that the objective function is nonconvex and the global convergence of the restricted Broyden family method is established. Preliminary numerical results including the classical optimization problems and the Muskingum model show that the presented algorithm is promising.

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Acknowledgements

The authors would like to thank the editor and the referees for their valuable comments which greatly improve this paper.

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Authors and Affiliations

  1. College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, People’s Republic of China

    Gonglin Yuan, Zhan Wang & Pengyuan Li

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  1. Gonglin Yuan
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  2. Zhan Wang
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  3. Pengyuan Li
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Correspondence to Gonglin Yuan.

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This work was supported by the National Natural Science Foundation of China (Grant No. 11661009), the High Level Innovation Teams and Excellent Scholars Program in Guangxi institutions of higher education (Grant No. [2019]52), the Guangxi Natural Science Key Fund (No. 2017GXNSFDA198046), and the Special Funds for Local Science and Technology Development Guided by the Central Government (No. ZY20198003).

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Yuan, G., Wang, Z. & Li, P. A modified Broyden family algorithm with global convergence under a weak Wolfe-Powell line search for unconstrained nonconvex problems. Calcolo 57, 35 (2020). https://doi.org/10.1007/s10092-020-00383-5

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